that bias in traditional population size estimators can be substantial because misidentification is ignored, and our new estimators perform well in

Transcription

1 Abstract YOSHIZAKI, JU. Use of atural Tags in Closed Population Capture-Recapture Studies: Modeling Misidentification. (Under the direction of Kenneth H. Pollock and icholas M. Haddad.) Estimates of demographic parameters such as population size, survival rates, and movement rates are often obtained by use of capture-recapture models. Capture-recapture methods usually reuire the capturing and marking of animals. These marks allow us to identify animals upon their recapture and create uniue capture histories for each animal captured. Then, parameter estimates are obtained based on modeling the capture histories. Traditionally, marks or tags are applied by researchers (applied tags). However, in recent years, naturally existing features of animals have also been used as tags in capture-recapture studies (natural tags). Our research focuses on the use of natural tags as an alternative to applied tags in closed population capture-recapture studies. We consider plausible misidentification mechanisms for individual-level natural tags and describe in detail how misidentification leads to errors in the observed capture history data. Effects on the observed capture history data may differ depending on how errors are introduced because the misidentification mechanism may vary depending on the type of natural tag and specific features of the study design. We found that the typical multinomial approach to model capture history data is not applicable when misidentification is possible, and it is important to clearly define the misidentification mechanism in a particular study to model misidentification appropriately. We first consider misidentification when using genetic tags in closed population capturerecapture studies (non-evolving natural tags 1). We then focus on the use of photographic tags, where two different types of errors are considered: those related to uality of photographs (nonevolving natural tags 2) and those related to changes in natural marks (evolving natural tags). For each type of misidentification mechanism, we develop a new closed population model that is applicable to that specific case and estimators based on uadratic distance functions. The models can be viewed as extensions of the traditional closed capture-recapture model that allows time variation in capture probabilities. Our goal is to present a clear framework for each misidentification mechanism and give its statistical model development. Through simulation studies, we show

2 that bias in traditional population size estimators can be substantial because misidentification is ignored, and our new estimators perform well in terms of both bias and precision provided capture probability is not too low. For non-evolving natural tags 1, we also present an alternative estimation method, which is based on likelihood theory, by conditioning on the capture histories that have two or more capture events. With the likelihood-based approach, only part of data can be used, and capture probabilities and misidentification rate cannnot be estimated separately. However, population size can be estimated as a derived parameter, and through simulation study, we show that this likelihood-based estimation method is of comparable accuracy to the uadratic methods that use all of the capture history data, except in cases with low capture probabilities where the uadratic distance estimators perform better. We also consider a variation of the basic model in which we allow for behavioral response, but no time variation, with possible misidentification. We show that population size is overestimated when misidentification is ignored, and performance of our new estimators is good provided capture probability is not too low. Finally, we discuss augmentation of capture history data with extra data on the misidentification rate. We particularly consider use of supplemental data obtained when identification is performed multiple times independently (multiple identification), and develop a model that allows us to utilize the augmented data. Although we demonstrate the benefit of the supplemental data for the cases where capture probability is low, in cases where capture probability is high, the benefit of supplemental data is less apparent and reuires future investigation.

3 USE OF ATURAL TAGS I CLOSED POPULATIO CAPTURE-RECAPTURE STUDIES: MODELIG MISIDETIFICATIO BY JU YOSHIZAKI A DISSERTATIO SUBMITTED TO THE GRADUATE FACULTY OF ORTH CAROLIA STATE UIVERSITY I PARTIAL FULFILLMET OF THE REQUIREMETS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BIOMATHEMATICS AD ZOOLOGY RALEIGH, ORTH CAROLIA APRIL 25, 27 APPROVED BY: KEETH H. POLLOCK CHAIR OF ADVISORY COMMITTEE ICHOLAS M. HADDAD CO-CHAIR OF ADVISORY COMMITTEE CAVELL BROWIE MIOR REPRESETATIVE JOSEPH E. HIGHTOWER JAMES D. ICHOLS

4 ii Biography Jun was born in Kuwana, Mie, a small town in central Japan, to Hiroyuki and Yukiko Yoshizaki. After graduating Kuwana high school in 199 and spending some time training as an euestrian in Belgium, she came to the United States in 1992 to begin university. She graduated from Virginia Polytechnic Institute and State University in 1997 with B.S. in Biology. From , she was an intern at the Cetacean Behavioral Lab at San Diego State University. In 1998, she started graduate school in Wildlife and Fisheries Science at the University of Tennessee, Knoxville and transferred to orth Carolina State University in 21 to focus on uantitative aspects of ecological studies. She earned a Master in Biomathematics in May 23 and continued graduate school at orth Carolina State University co-majoring in Biomathematics and Zoology.

5 iii Acknowledgements This work would have been impossible without the contributions of my committee and the support of family and friends. I would like to thank my advisor, Ken Pollock, whose support and encouragement has been greatly appreciated from the beginning. I would also like to thank Cavell Brownie for providing me with strong statistical insights. The discussions with Ken and Cavell have proven invaluable in synthesizing the concepts that are developed herein. I would also like to thank committee members ick Haddad, Joe Hightower and Jim ichols for their help on this project. Their advice has been extremely important and is incorporated throughout. In addition, I would like to thank Bill Kendall, Mike Runge, and Kyle Shertzer for opportunities to work on various projects during summer internships; Bill Link, Larissa Bailey, and Don Church for their ideas on this project; Tim Langer for graciously allowing me to use his data set; my parents in Japan for their encouragement; many wonderful friends, especially, Ray, Sunny, Suzanne, Geoff, Darren, Aiko, and Dino; Jason and James at Reverie for providing me a comfortable workspace; and my cat Kumo for being with me through many long nights.

6 iv Contents List of Figures... List of Tables... vi vii 1 Use of atural Tags in Capture-Recapture Studies Introduction Conventional Capture-Recapture Models Tags Types of Tags Level of Identification Tag-Related Assumptions Special Issues with atural Tags Individual-LevelaturalTags Overview Potential Assumption Violations Modeling Misidentification Population-Level atural Tags Discussion Bibliography on-evolving atural Tags 1: Possible Misidentification at Any Capture Introduction Lukacs and Burnham Misidentification Model Proposed Misidentification Mechanism Statistical Model Development Model Formulation and Simple Examples Estimation Simulation Study Simulation 1: Cases with Time Specific Capture Probabilities Simulation 2: Cases with Time Specific Capture Probabilities (High ) Simulation 3: Cases with Constant Capture Probability Simulation 4: Estimated Generalized Least Suares Method Discussion Bibliography... 71

7 v 3 Extensions of Model E Introduction Likelihood-Based Estimation Method Statistical Model Development and Estimation Simulation Study: Conditional Likelihood Estimation Method Model E1 with Behavioral Responses Statistical Model Development and Estimation Simulation Study: Cases with Behavioral Responses Supplemental Data from Multiple Identification Statistical Model Development and Estimation Simulation 1: Application of Multiple Identification to E1 t Simulation 2: Application of Multiple Identification to E1 b Discussion Bibliography Photographic Tag-based Capture-Recapture Studies: Models E2 and EV Introduction on-evolving atural Tags 2: Misidentification is Possible Only at Recaptures Proposed Misidentification Mechanism Statistical Model Development Estimation Simulation Study EvolvingaturalTags Proposed Misidentification Mechanisms Statistical Model Development Estimation Simulation Study Discussion Bibliography Appendix A Summaries of the Marginal Probabilities in a 5-Sample Study

8 vi List of Figures 1.1 A summary diagram of tag types commonly used in capture-recapture studies A summary diagram of issues with use of natural tags in capture-recapture studies A diagram of the misidentification mechanism for non-evolving natural tags A diagram of the misidentification mechanism for non-evolving natural tags 1 with behavioralresponse A diagram of the misidentification mechanism for non-evolving natural tags A diagram of the misidentification mechanism for evolving natural tags

9 vii List of Tables 1.1 A summary of terms used to define types of tags and types of capture histories A summary of notation used for misidentification models A summary of the observable capture histories, γ, and associated probabilities for non-evolving natural tags 1 for the 3-sample case A summary of the marginal probabilities of the observable capture histories, γ, for non-evolving natural tags 1 in a 3-sample study [Simulation 1: case 1] on-evolving natural tags 1 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 1: case 2] on-evolving natural tags 1 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 1: case 3] on-evolving natural tags 1 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 1: case 4] on-evolving natural tags 1 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 2: case 1] on-evolving natural tags 1 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all )approach [Simulation 2: case 2] on-evolving natural tags 1 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all )approach [Simulation 2: case 3] on-evolving natural tags 1 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all )approach

10 viii 2.11 [Simulation 2: case 4] on-evolving natural tags 1 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all )approach [Simulation 3: case 1] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 are from the conditional (on x all ) approach [Simulation 3: case 2] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 are from the conditional (on x all ) approach [Simulation 3: case 3] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 are from the conditional (on x all ) approach [Simulation 3: case 4] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 are from the conditional (on x all ) approach [Simulation 3: case 1] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 3: case 2] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 3: case 3] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach [Simulation 3: case 4] on-evolving natural tags 1 with constant capture probability. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 t are from the conditional (on x all ) approach A summary of the latent capture histories, δ, and associated probabilities for nonevolving natural tags 1 for the 3-sample case [Simulation 4: cases 1 and 2] on-evolving natural tags 1. Average estimates (with standard errors in parentheses) based on 1 simulated data sets under Model E1 t [Simulation 4: cases 3 and 4] on-evolving natural tags 1. Average estimates (with standard errors in parentheses) based on 1 simulated data sets under Model E1 t A summary of the probabilities of the observable capture histories under Model E1 t conditional on the capture histories that have two or more capture events, γ, ina3-samplestudy [Simulation Study: case 1] E1 t with likelihood-based estimation method. Average estimates (with standard errors in parentheses) under Model E1 t. Estimates are based on 1 simulated data sets [Simulation Study: case 2] E1 t with likelihood-based estimation method. Average estimates (with standard errors in parentheses) under Model E1 t. Estimates are based on 1 simulated data sets.... 8

11 3.4 [Simulation Study: case 3] E1 t with likelihood-based estimation method. Average estimates (with standard errors in parentheses) under Model E1 t. Estimates are based on 1 simulated data sets [Simulation Study: case 4] E1 t with likelihood-based estimation method. Average estimates (with standard errors in parentheses) under Model E1 t. Estimates are based on 1 simulated data sets A summary of the observable capture histories, γ, and associated probabilities for non-evolving natural tags 1 with behavioral response for the 3-sample case A summary of the marginal probabilities of the observable capture histories, γ, for non-evolving natural tags 1 with behavioral response in a 3-sample study [Simulation Study: case A] on-evolving natural tags 1 with behavioral response. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 b are from the conditional (on x all ) approach [Simulation Study: case B] on-evolving natural tags 1 with behavioral response. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 b are from the conditional (on x all ) approach [Simulation Study: case C] on-evolving natural tags 1 with behavioral response. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E1 b are from the conditional (on x all ) approach [Simulation 1: case 1] Application of multiple identification to E1 t. Average estimates (with standard errors in parentheses) under the Model E1 t,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification [Simulation 1: case 2] Application of multiple identification to E1 t. Average estimates (with standard errors in parentheses) under the Model E1 t,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification [Simulation 1: case 3] Application of multiple identification to E1 t. Average estimates (with standard errors in parentheses) under the Model E1 t,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification [Simulation 1: case 4] Application of multiple identification to E1 t. Average estimates (with standard errors in parentheses) under the Model E1 t,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification [Simulation 2: case A] Application of multiple identification to E1 b. Average estimates (with standard errors in parentheses) under the Model E1 b,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification [Simulation 2: case B] Application of multiple identification to E1 b. Average estimates (with standard errors in parentheses) under the Model E1 b,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification ix

12 x 3.17 [Simulation 2: case C] Application of multiple identification to E1 b. Average estimates (with standard errors in parentheses) under the Model E1 b,. Estimates are based on 1 simulated data sets, and n indicates the sample size used for multiple identification A summary of the observable capture histories and associated probabilities for nonevolving natural tags 2 for the 3-sample case A summary of the marginal probabilities of the observable capture histories, γ, for non-evolving natural tags 2 in a 3-sample study [Simulation 1: case 1] on-evolving natural tags 2 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all ) approach [Simulation 1: case 2] on-evolving natural tags 2 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all ) approach [Simulation 1: case 3] on-evolving natural tags 2 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all ) approach [Simulation 1: case 4] on-evolving natural tags 2 with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all ) approach [Simulation 2: case 1] on-evolving natural tags 2 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all )approach [Simulation 2: case 2] on-evolving natural tags 2 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all )approach [Simulation 2: case 3] on-evolving natural tags 2 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all )approach [Simulation 2: case 4] on-evolving natural tags 2 with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model E2 t are from the conditional (on x all )approach A summary of the observable capture histories and associated probabilities for evolving natural tags for the 3-sample case A summary of the marginal probabilities of the observable capture histories, γ, for evolving natural tags in a 3-sample study

13 xi 4.13 [Simulation 1: case 1] Evolving natural tags with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 1: case 2] Evolving natural tags with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 1: case 3] Evolving natural tags with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 1: case 4] Evolving natural tags with time specific capture probabilities. Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 2: case 1] Evolving natural tags with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 2: case 2] Evolving natural tags with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 2: case 3] Evolving natural tags with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach [Simulation 2: case 4] Evolving natural tags with time specific capture probabilities (high ). Average estimates (with standard errors in parentheses) based on 1 simulated data sets. Estimates under Model EV t are from the conditional (on x all ) approach A.1 A summary of the marginal probabilities of the observable capture histories, γ, for non-evolving natural tags 1 in a 5-sample study A.2 A summary of the marginal probabilities of the observable capture histories, γ, for non-evolving natural tags 2 in a 5-sample study A.3 A summary of the marginal probabilities of the observable capture histories, γ, for evolving natural tags in a 5-sample study

14 1 Chapter 1 Use of atural Tags in Capture-Recapture Studies 1.1 Introduction Estimates of demographic parameters such as population size, survival rates, recruitment rates and movement rates are often obtained by use of capture-recapture models (Williams et al., 22). Capture-recapture methods usually reuire the capturing and marking of animals. These marks allow us to identify animals upon their recapture, and create uniue capture histories (e.g. [11], [1], etc) for each animal captured. Parameter estimates are obtained based on modeling the capture histories. These parameter estimates are crucial to building sound population dynamics models, and they may be used in scientifically based management of many wildlife and fisheries populations. Capture-recapture models are of many types depending on the study design, and the data structure and parameters of interest may differ among models. In this chapter, we present a very brief overview of different types of capture-recapture models and properties of tags used to mark animals. We then outline issues that arise with use of natural tags in capture-recapture studies, paying particular attention to the issue of misidentification. 1.2 Conventional Capture-Recapture Models Conventional capture-recapture models are either closed or open models. Estimation of population size is the focus of closed population models. These models do not allow additions (i.e.,

15 Chapter 1. Use of atural Tags in Capture-Recapture Studies 2 births or immigrants) or deletions (i.e., deaths or emigrants) of animals from the population during the study so that the population is constant during the whole study. The 2-sample closed population model, often referred to as the Lincoln-Petersen model, is the simplest capture-recapture model, and this model assumes eual capture probability for all animals in the population on each sampling occasion. The assumption of eual capture probability can be relaxed with K-sample closed population models where K>2, which allow for varying capture probabilities due to individual heterogeneity, behavioral response, time variation or combinations of these (Otis et al., 1978; Pollock et al., 199; Williams et al., 22). Open population models allow additions or deletions of animals from the population during the study. The general Jolly-Seber model has K>2sampling occasions, and population size, survival rates and recruitment rates can be estimated (Jolly, 1965; Seber, 1965, 1982; Williams et al., 22). The Cormack-Jolly-Seber model is based on a component of the Jolly-Seber model that focuses on the estimation of survival parameters, and uses the data conditioned on first capture (Cormack, 1964; Lebreton et al., 1992; Williams et al., 22). Another class of models comprise the tag-return models of Brownie et al. (1985), in which tags are usually returned by harvesters. This set of models is related to, but distinct from, the Cormack-Jolly-Seber model with multiple capture events because animals can be recaptured only once, but again the main focus is on the estimation of survival parameters. Multistate models, which can be considered as another extension of Cormack-Jolly-Seber model, have wide applications in capture-recapture and tag-return studies. Under these models we assume that there are groups of animals in different states (e.g., populations in different locations, animals in different status of breeding), and the focus is estimation of parameters that are related to transitions between different states (e.g., movements from location A to location B, changes from breeder to nonbreeder) in addition to survival parameters (Arnason, 1972; Hestbeck et al., 1991; Brownie et al., 1993; Schwarz et al., 1993; Williams et al., 22). The Robust design is another important area of capture-recapture modeling, which provides data from both closed and open populations. The robust design has two different types of sampling periods, primary and secondary. Each primary sampling period has a set of secondary sampling periods nested within it, and primary periods have long intervals between them and assume an open population structure, whereas the secondary periods have short intervals between them and assume a closed population structure within each primary period. The robust study design allows

16 Chapter 1. Use of atural Tags in Capture-Recapture Studies 3 us to: allow for uneual catchability of animals; estimate parameters that cannot be estimated by closed or open population models alone such as temporary emigration; and improve the precision of parameter estimates (Pollock, 1982; Kendall et al., 1997; Williams et al., 22). 1.3 Tags Types of Tags Different types of marking methods can be used to obtain capture-recapture data, and here a tag refers to any feature that can be used to identify individuals or groups of animals. Many of the conventional tags used in capture-recapture studies are applied to animals by investigators, and we refer to them as applied tags. Traditionally capture-recapture methods are based on applied tags (Seber, 1982), and there are many different types of tags depending on the animals being studied. Some examples of applied tags include physical devices or modification of the animals, such as numbered bands, radio tags, satellite tags, or tattoos. In capture-recapture studies, applied tags have many advantages because tags can be designed to suit the purpose of the study, and are in many ways under the researchers control. On the other hand, there are aspects of applied tags that are not desirable. Of particular concern is the necessity to physically capture animals to apply the tags, which may be very problematic if the species of interest is elusive or expensive to physically capture. Also, physically attaching tags to animals can cause various problems such as discomfort and infection, which can affect survival and capture probability. Further, applied tags may be lost during the study. On the other hand, naturally existing features of animals (natural marks) can also be used to mark animals, and we refer to tags based on natural marks as natural tags. Visible features of animals such as variation in stripe patterns on tigers and scars on manatees (e.g., Pennycuick, 1978; Hammond, 1986; Karanth et al., 24b; Langtimm et al., 24) have been widely used as tags by taking their photographs, which we refer to as photographic tags, and use of photographic tags has been an important area of capture-recapture research (e.g., Agler, 1992; Bain, 1992; Durban et al., 25). Recently, advances in technology have opened the use of natural tags to a wider range of ecological studies, and there is now a growing body of literature on the use of different types of natural tags instead of applied tags. For example, techniues developed in forensic science allow

17 Chapter 1. Use of atural Tags in Capture-Recapture Studies 4 us to use genotypes to mark animals, which we refer to as genetic tags (also DA fingerprints) (Waits, 24). Such techniues are currently used in many capture-recapture studies (Waits and Paetkau, 25), and are another important area of capture-recapture research (e.g., Mills et al., 2; Gosky, 24; Lukacs, 25; Lukacs and Burnham, 25). There are many other types of natural marks that can be used as tags as well (e.g., otolith chemistry), but in our discussion we shall mainly focus on use of photographic tags and use of genetic tags. atural tags are less invasive than applied tags because it is often not necessary to physically capture the animals. Therefore, natural tags might appear to be more advantageous in capturerecapture studies. This may be true in some cases, however, there are aspects of using natural tags that lead to new challenges that were not faced when using applied tags. Such new challenges can be summarized into three main issues: 1. uncertainty in the level of identification; 2. misidentification or misclassification; and 3. unmarkable animals. We are left with the common dilemma in decision making of trade-offs, and to assess these tradeoffs, it is necessary to have a very clear framework for the modeling of capture-recapture data based on natural tags and the assumptions involved. In later sections, we will discuss each issue briefly Level of Identification It is also important to consider the level of identification that can be achieved by use of the tags. In capture-recapture studies, the necessary level of identification of animals differs depending on the purpose of study. For example, some studies only need to identify groups of animals that share some aspect of their life history in common (e.g., fish from the same natal river) whereas others reuire identification of individual animals. Tags that only allow us to identify groups of animals that share some aspect in common are referred to as population-level tags. Those that allow us to identify each individual animal are referred to as individual-level tags. Colored bands, patterns in gene expression and otolith microchemistry are good examples of population-level tags

18 Chapter 1. Use of atural Tags in Capture-Recapture Studies 5 Table 1.1: A summary of terms used to define types of tags and types of capture histories. Glossary Tags Applied tags atural tags Genetic Tags Photographic Tags Population-level tags Individual-level tags on-evolving natural tags Evolving natural tags True capture history Observable capture history Real capture history Ghost capture history Any features that can be used to identify animals Tags that are applied by investigators Tags based on naturally existing features of animals Example of natural tags; obtained from analyses of DA samples Example of natural tags; use visible uniue feature of animal Tags that can be used to identify groups of animals only Tags that can be used to identify individual animals atural tags that are not likely to change over time atural tags that can change over time Capture history that corresponds to capture events, and unknown when there is possible misidentification Capture history that can be observed Capture history that belongs to existing animals and may or may not contain misidentification Capture history that belongs to non-existing animals, and is created by misidentification whereas individually numbered bands, coloration patterns and genotypes are good examples of individual-level tags. A glossary of terms used is presented here to aid the reader (Table 1.1) Tag-Related Assumptions There are several underlying assumptions, not always explicitly stated, in capture-recapture studies that are specific to the properties of tags. These are relevant to both applied and natural tags. Conventional capture-recapture models assume that: 1. All captured animals can be tagged in some way; 2. The tags do not affect survival;

19 Chapter 1. Use of atural Tags in Capture-Recapture Studies 6 3. The tags are not lost or modified during the study; 4. The tags are uniue to the level of interest (e.g., population- or individual-level); and 5. The tags allow correct identification of captured animals. These assumptions plus additional assumptions about capture probabilities are necessary to obtain estimates that are unbiased. Any violation of these assumptions can have serious conseuences. Thus, properties of tags are an important aspect of capture-recapture studies, and assumptions that are more or less likely to be violated may differ among different tag types. We shall explore violation of these assumptions in detail as they relate to the use of various types of natural tags in later sections Special Issues with atural Tags Traditionally in capture-recapture studies, investigators assume that the level of identification (i.e., population- or individual-level) is known, and information to identify animals at the level of interest is known with certainty. This is particularly true with applied tags. For example, we know that individually numbered bands can be used to uniuely identify marked individuals and that the identification number that is applied to each captured animal is known with certainty. In other words, we can have a catalog of tags in which the identification information on the tags is known with certainty. However, natural tags often do not allow us to have identification information that is certain. For example, a catalog of each captured animal s genotype (i.e., DA fingerprints) may be obtained by analyzing the DA sample upon capture events. Two problems with identification are possible here: the genotype may not contain enough information to distinguish each animal in the population (Mills et al., 2; Gosky, 24), and the DA fingerprint may contain errors due to faulty field or laboratory work (Lukacs and Burnham, 25). The former problem causes the situation in which multiple animals share the same genotype, thus the tag should not be used for individual identification (uncertainty in the level of identification). The latter problem causes the situation that the tag information is incorrect, thus it can lead to incorrect identification of individual animals when tags are used at the individual-level (misidentification), or to incorrect status when tags are used at the population-level (misclassification).

20 Chapter 1. Use of atural Tags in Capture-Recapture Studies 7 These are new challenges we have with natural tags, and the resulting violations of the assumptions of conventional capture-recapture models may lead to large biases in parameter estimates. In the next section, we focus on use of individual-level natural tags, and explore potential violations of conventional capture-recapture model assumptions and their effects on capture-recapture data in general. 1.4 Individual-Level atural Tags Overview There are many types of natural marks of animals that can be used to mark individual animals, however, individual-level natural tags can be classified into two main categories: genetic tags and photographic tags. We will focus closely on these two types of individual-level natural tags to illustrate potential issues. Genetic tag-based capture-recapture studies typically involve collection of physical material in the field (e.g., blood, skin or hair) that contains the animal s DA, extraction of DA, and amplification of the DA to obtain DA fingerprints (or genetic tags) using a techniue called polymerase chain reaction (PCR). Each captured individual can then be identified based on the DA fingerprint (Waits, 24), which allows us to construct capture histories of animals in the population. The second type of study uses uniue visible features of animals, and there are many variations in natural marks that can be used (e.g., coloration patterns and injury scars). These studies often employ a photographic identification techniue, which typically involves taking photographs of the natural marks in the field. Then, identification is performed based on the photographic records of natural marks (photographic tags) (Karanth et al., 24a). Matching of newly photographed natural marks to the ones in photographs from previous sampling occasions indicates a recapture event, while non-matching indicates a first capture event. In some cases and particularly with terrestrial species, sampling is automated by setting camera traps in the fields (e.g., tigers in Karanth, 1995). In other cases, and particularly with highly visible auatic species such as marine mammals, photographs are taken based upon visual encounters during field surveys (e.g., manatees in Langtimm et al., 24). The brief summary of types of natural tags is shown in Figure 1.1.

21 Chapter 1. Use of atural Tags in Capture-Recapture Studies 8 Applied tags Tags atural tags on-evolving Evolving Genetic Photographic (e.g. coloration patterns) Photographic (e.g. injury scars) Figure 1.1: A summary diagram of tag types commonly used in capture-recapture studies Potential Assumption Violations Misidentification Theoretically, genetic tags possess good properties as a tag in capture-recapture studies because: all animals can be tagged; the tag is uniue to an individual animal; and there is no loss or modification of the tag. However, there are a number of potential problems associated with use of this method in practice. The uality of the samples, which can be affected by field techniues and storing methods, can cause errors in the DA fingerprints. Also, errors in DA fingerprints can be introduced in the laboratory (Taberlet et al., 1999; Waits, 24; Waits and Paetkau, 25). If the DA fingerprints contain errors for any reason, they lead to incorrect identification of individual animals (violation of assumption 5). Similarly, misidentification of animals is possible with photographic tag-based studies, which can be caused by a number of factors. For example, less distinctive natural marks or poor uality photographs may increase the risk of errors during the process of matching photographs. In addition, unlike genetic tags, some visible natural marks are not consistent over time, for example, scars are subject to loss or modification over time (e.g., Carlson et al., 199), possibly making the misidentification issue more complicated (violation of assumption 3). Whether a certain type of natural tag can be lost or modified over time is an important aspect of misidentification, and here we make a division of natural tags into two different types.

22 Chapter 1. Use of atural Tags in Capture-Recapture Studies 9 We refer to natural tags that are not likely to change over time as non-evolving natural tags, and those that can change over time as evolving natural tags. For example, it is reasonable to consider that genetic tags and photographic tags that use coloration patterns like stripes on tigers are non-evolving natural tags, but photographic tags that use injury scars on species like manatee are evolving natural tags in long-term studies. However, whether a certain type of natural tag is non-evolving or evolving needs to be justified for each study based on considerations such as the specific natural tag involved, the sampling design, and the duration of study. ote that minimization of such errors should be an important goal of any study, and there has been research on field and laboratory techniues to minimize genotyping errors (Waits and Paetkau, 25; Taberlet and Luikart, 1999) and on methods to uantify the magnitude of errors in DA fingerprints (Bonin et al., 24; McKelvey and Schwartz, 24; Buchan et al., 25). For studies that use photographic tags, there are now detailed protocols to avoid mismatching of photographs (e.g., Defran et al., 199), and computer programs have been developed to aid the matching process (e.g., Arzoumanian et al., 25). However, misidentification may never be eliminated completely. Thus, in addition to the effort to minimize errors that lead to misidentification, it is important to develop models that allow misidentification in order to analyze natural tag-based capture-recapture data. Uncertainty in the level of identification Another potential challenge is uncertainty in the level of identification (violation of assumption 4). For example, in genetic tag-based capture-recapture studies, the genotype would not provide enough information to identify individuals if the number of loci examined is too small, leading to a situation in which a number of individuals share the same genotype (Taberlet and Luikart, 1999; Waits, 24). Thus, it would be only possible to identify groups of individuals within the population. In such cases, genotype should be treated as a population-level tag, but information such as the number of distinct genotypes in the population and the number of animals that share each genotype is unknown, and thus need to be estimated. This problem is often referred to as the shadow effect, and data should be analyzed with a model that incorporates such uncertainty (Mills et al., 2; Gosky, 24) (see also Figure 1.2). Uncertainty in level of identification can also be a problem in photographic tag-based studies.

23 Chapter 1. Use of atural Tags in Capture-Recapture Studies 1 For example, there may be animals that possess similar injury scars, making them difficult to distinguish. Therefore, we cannot be absolutely sure that these natural marks are uniue to each animal (Pennycuick, 1978). This problem should be avoided by carefully choosing which natural marks should be used in the study or by using multiple natural marks for identification so that animals are identified correctly to the level of the investigators interests and needs. Unmarkable animals In photographic tag-based studies, it may be the case that we have unmarkable animals (violation of assumption 1). For example, there may be animals that do not possess distinct injury scars or young animals in which natural marks have not yet fully developed. Unmarkable animals cannot be followed to construct their capture histories due to lack of identifiable natural marks, and the only data we can obtain from them are total number of photographs taken at each sampling occasion. Conseuently, if data on unmarkable animals are ignored, estimates are only applicable to the markable portion of the population, similar to the case of uncatchable animals for a particular trapping method (Seber, 1982). In some studies, unmarkable animals are a serious problem, for example, the majority ( 7%) is considered as unmarkable in bowhead whale populations, and special capture-recapture models that incorporate unmarkable animals have been developed (Da Silva et al., 2, 23) Modeling Misidentification Although misidentification can occur with applied tags (e.g., as when numbers on leg bands are misread), the potential for misidentification is greater and a more serious problem when natural tags are used in capture-recapture studies. It is important to remember that there is always a risk of misidentification with individual-level natural tag-based capture-recapture studies. Such data should be analyzed using models in which an appropriate misidentification mechanism for the data is incorporated. However, it is often difficult to identify the appropriate misidentification mechanism, and here we give a simple example of a capture-recapture study to illustrate necessary considerations and the effects of misidentification on observed capture-recapture data.

24 Chapter 1. Use of atural Tags in Capture-Recapture Studies 11 Who is identified through misidentification? Consider a single sampling occasion. Suppose an animal A is captured. Then, identification of animal A can be either correct or incorrect. If identification of the animal was incorrect, then the uestion is whose identity is assigned to animal A. In some cases correct identification of marked animals may not be possible even with applied tags, for example, if the last digit of the identification number on the tag is lost. However unless the tags are completely lost, investigators can identify the problematic tags because they know the identification numbers applied to previously captured animals. Thus, this type of misidentification can be removed from capture-recapture data when applied tags are used. There are other situations where misidentification of applied tags occurs but is not recognized, for example, when tags are read from a distance and misidentified as another tag. In such cases, incorrect identification always leads to false identification of other animals in the population that have already been captured. Schwarz and Stobo (1999) termed this problem tagmisread, investigated its effect in capture-recapture studies, and developed models to estimate tag-misreading rates. On the other hand, with natural tags, it is not known when an identification error has occurred, and misidentification cannot be restricted to cases that lead to false identification of existing previously marked animals in the population. In other words, misidentification of an animal can lead to two types of error: (1) assigning the identity of an animal in the population to a different animal, and (2) assigning an identity that does not exist to a new capture or to a recaptured animal. The conseuences of misidentification in capture-recapture data differ depending on the assumptions made concerning the mechanisms of misidentification. For example, assigning the identity of a previously tagged animal to an existing animal in the population results in the combining of capture histories of two animals, whereas assigning a non-existing identity to a captured animal results in splitting of the capture history of an animal into multiple capture histories. Theoretically, any type of misidentification can occur with natural tags. However considering all possible ways that errors in identification can be introduced, there are numerous different effects of misidentification on the observed capture history data, and hence on parameter estimates from traditional models that assume no misidentification. We believe that it is not practical to consider all possible scenarios and incorporate them into capture-recapture models. Thus, it is important

25 Chapter 1. Use of atural Tags in Capture-Recapture Studies 12 to identify the mechanisms of misidentification that are most likely to occur in the study, make appropriate assumptions, and develop models based on the assumptions. For example, Lukacs and Burnham (25) studied the particular case of misidentification when genetic tags are used. They assumed that misidentification leads only to creation of non-existing animals based on the fact that the number of possible genotypes greatly exceeds the number of individuals in the population, and that errors in a DA fingerprint are unlikely to generate a fingerprint that matches that of another existing animal in the population. This assumption seems to be reasonable for the case of genetic tags, and it also helps to simplify the issue of misidentification. When can misidentification occur? Another aspect that needs to be considered is whether misidentification is possible at all sampling occasions or not. Identification errors in photographic tag-based studies are likely to be due to matching errors when newly taken photographs are compared to previously taken photographs, and therefore may not apply to the first capture event. However with certain types of natural tags, we should include the possibility of misidentification when animals are captured for the first time. For example, the likelihood of errors in DA fingerprints does not depend on whether the animal is a first-time capture or a recapture, and misidentification can occur at both first capture and recapture events. Conseuently, it is again important to consider how errors in identification can be introduced during the study to model misidentification appropriately. Can errors be repeated? It is also important to consider whether the same identification error can occur more than once during the study. Theoretically, the same false identity can be created on one or more sampling occasions for the same animal or for multiple different animals. The resulting effects on capture-recapture data differ depending on how repeated errors can occur during the study. The simplest case is to assume that an error is never repeated, and we term this situation as uniue identification errors. This may be an oversimplification, but may be necessary to keep models parsimonious and useful for estimation.